Structuring of suspended sediments in periodic vortex flow over a vortex ripple

The formation of spatially ordered structures in a suspended sediment under the action of two-dimensional standing surface gravity waves is studied experimentally for the first time in a rectangular vessel oscillating in the vertical direction. The parameters of the structured regions in vessels with individual vortex ripples and groups of ripples are found for the first and second wave modes. Isolated structured regions of the suspended sediment appear over the bottom topography and gradually reach the free surface. The corresponding spatial horizontal scales are determined by the sand ripple dimensions, while the vertical scale of the clouds increases with time. In all experiments, the structures formed remained unchanged during the whole interval of the fluid wave motion and disappeared when the parametric excitation of the waves stopped.     

ON REICH''''S OPEN QUESTION

1　IntroductionandPreliminariesThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E → 2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E ,　〈x ,f〉 =‖x‖‖f‖ ,　‖x‖ =‖f‖ 　 (x∈E) . (1 )　　Definition 1　LetT :D →Dbeamapping .1 .Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞ )withlimn→∞kn =1suchthat‖Tnx-Tny‖ ≤kn‖x-y‖　forall　x ,y∈D ,n≥ 1 ;　　 2 .Tissaidtobenonexpansive,ifthesequence kn app…     

Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers

A three-dimensional study of suspension of drops in simple shear flow has been performed at finite Reynolds numbers. Results are obtained using a finite difference/front tracking method in a periodic domain. The effects of the Reynolds number and the Capillary number are addressed at two volume fractions: 0.195 and 0.34. It is observed that suspensions of deformable drops exhibit a shear-thinning behavior. Similar to the motion of a single drop, drops migrate away from the walls. The effective viscosity, the first and the second normal stress differences oscillate around a mean value in all cases. The first normal stress difference increases with the Capillary number, the Reynolds number and the volume fraction. Results show that drops deform more and orient more in the flow direction as the Capillary number or the volume fraction is increased. Also, the average size of clusters is smaller than for suspension of rigid particles. The radial dependence of the pair distribution function across the channel has been studied. This dependency shows that the tendency to form clusters is reduced as the Capillary number increases or the volume fraction decreases.     

An accurate computation for rapidly varied flow in an open channel

A new method combining the Preissmann four-point scheme and the Holly–Preissmann reach-back scheme is introduced to solve the rapidly varied flow problem in an open channel. The Preissmann four-point scheme is well known for the computation of one-dimensional unsteady flow. The Holly–Preissmann reach-back scheme integrates the Holly-Preissmann two-point scheme with the concept of reach-back characteristics, which allows the characteristics to project several time steps beyond the current time level. A spontaneous surge formation case is used to demonstrate and evaluate the applicability of the new method. It has been found that the results from this method are quite compatible with those of Preissmann four-point scheme. In addition, with the appropriate choice of the number of reach-back time steps, this new method can always avoid the numerical oscillation which usually exists when one uses the Preissmann four-point scheme for the condition of Courant number not close to unity.     

Hydromagnetic Stokes flow in a rotating fluid with suspended small particles

An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.     

UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION

The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇ s open question is given. The results presented extend and improve Zhang Shisheng＇ s recent ones in the following aspects ： （i） Zhang＇ s stronger condition that the sequence of iterative parameters converges to zero is removed; （ii） Zhang＇ s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （iii） Zhang＇ s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.     

Experimental and numerical study of the rotation and the erosion of fillers suspended in viscoelastic fluids under simple shear flow

When a porous agglomerate immersed in a fluid is submitted to a shear flow, hydrodynamic stresses acting on its surface may cause a size reduction if they exceed the cohesive stress of the agglomerate. The aggregates forming the agglomerate are slowly removed from the agglomerate surface. Such a behaviour is known when the suspending fluid is Newtonian but unknown if the fluid is viscoelastic. By using rheo-optical tools, model fluids, carbon black agglomerates and particles of various shapes, we found that the particles had a rotational motion around the vorticity axis with a period which is independent on shape (flat particles not considered), but which is exponentially increasing with the elasticity of the medium expressed by the Weissenberg number (We). Spherical particles are always rotating for We up to 2.6 (largest investigated We in this study) but elongated particles stop rotating for We>0.9 while orienting along the flow direction. Erosion is strongly reduced by elasticity. Since finite element numerical simulation shows that elasticity increases the local stress around a particle, the origin of the erosion reduction is interpreted as an increase of cohesiveness of the porous agglomerate due to the infiltration of a viscoelastic fluid.     

An experimental study of drop migration in shear flow between concentric cylinders

The phenomenon of migration of liquid drops in Couette flow between concentric cylinders due to non-Newtonian fluid properties and shape deformation has been studied experimentally. The results agree very well with the theory of Chan and Leal, which included the effect of hydrodynamic interaction with the bounding walls, and that of velocity profile curvature in a Couette device. Significant observations that were not reported in previous studies include the migration of a deformable Newtonian drop to an equilibrium position between the centerline and the inner rotor, and the competition between normal stresses and shape deformation effects for the case of a Newtonian drop in a non-Newtonian fluid.     

An investigation into the interfacial shear stress contribution in two-phase stratified flow

This paper provides a combined theoretical and experimental investigation into the contribution of interfacial shear stress in certain co and counter-current flows in circular pipes. Based on momentum balance two equations were developed for such flows then two fluid systems of significantly different density ratio were experimentally tested to quantify these equations.     

Viscous dissipation with fluid inertia in oscillatory shear flow

For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry.     

On long waves in shallow water with shear flow

Various evolution equations for long interfacial waves with shear flow are derived with the assumptions that: (1) the wavelength of the interfacial waves is much larger than the total depth of the fluids, and (2) that the spanwise dependence is much weaker than the streamwise dependence. A particular case of interest occurs when the interfacial waves are at or near direct resonance. In this case the Boussinesq equation replaces the Korteweg-de Vries equation. Various special solutions in two dimensions are discussed.     

Vortices in time-periodic shear flow

Vortices emerging in geophysical turbulence may experience deformations due to the non-uniform ambient flow induced by neighbouring vortices. At first approximation this ambient flow is modeled by a linear shear flow. It is well known from previous studies that the vortex may be (partially) destructed through removal of weak vorticity at the vortex edge—a process referred to as ‘stripping’. While most previous studies considered a stationary external shear flow, we have examined the behaviour of the vortex embedded in a linear shear flow whose strength changes harmonically in time. Aspects of the vortex dynamics and the (chaotic) transport of tracers have been studied by both laboratory experiments and numerical simulations based on a simple kinematical model.     

Elliptic cylinder in inviscid shear flow

We examine the flow of a plane parallel inviscid stream about an elliptic contour. There is vorticity far ahead of the body because of nonuniformity of the velocity profile. In the case of a small vorticity parameter the velocity profile will be parabolic. In contrast with [1] and [2], we assume the existence of additional circulational flow around the contour. The magnitude of this flow circulation is determined from the condition under which the flow leaves the trailing edge of the body (the analog of the Chaplygin-Zhukovskii postulate in potential flow).The results obtained in this study can be used, in particular, to evaluate the flow past a two-dimensional body in the wake behind another body.The author wishes to thank G. A. Dombrovskii for his interest in this study.     

Experimental study of shear flow instability

The results of experiments carried out in order to study the instability of a free shear layer of rotating barotropic fluid at high Reynolds numbers are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 167–173, May–June, 1992.     

Fundamental solutions in perturbed shear flow

In this paper infinite plane Couette flow in a viscous incompressible fluid is considered subject to general three-dimensional perturbations and the equations of motion are linearized. Furthermore, initial-value problems are posed and a set of closed-form solutions are obtained for a variety of conditions, such as the system under the influence of: (i) a mass source; (ii) an external force; or (iii) initial vorticity. The result is a knowledge of both the early transient dynamics and the near spatial field behavior, as well as the state after a long time and the far field behavior. It is shown that the solutions can be considered as fundamental (in the sense that source-sink solutions are regarded fundamental for irrotational motion) and therefore are useful in analyzing other boundary-value, initial-value problems where the basic flow can be synthesized from piece-wise linear (constant shear) variations. To this end a generalized Green's function for the system is determined.     

An interpretation of the stability of a turbulent shear flow near a rough wall

A conventional, small perturbation, stability analysis has been applied to a fully developed turbulent shear flow in a parallel duct with rough walls. This is an attempt to detect the inherent state of flow stability to quasi-regular disturbances emanating from the surface roughness elements. The surface roughness is represented by the usual roughness Reynolds number; it is fed into the analysis through an assumed mean velocity profile valid between the viscous sublayer and the inner (wall) region. An eddy viscosity model is used to secure the equation closure and the final equation for the perturbation amplitude has been solved numerically using the techniques developed for the Orr-Sommerfeld equation.Within the domain of realistic flow conditions, and for a range of surface roughness amplitudes, a local minimum of stability in terms of the longitudinal wave number has been found. However, it is not implied that it is a minimum minomorum, as only a limited range of surface roughnesses has been tried.